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Lectures on Generating Functions
 
S. K. Lando Independent University of Moscow, Moscow, Russia
Lectures on Generating Functions
Softcover ISBN:  978-0-8218-3481-7
Product Code:  STML/23
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-1819-9
Product Code:  STML/23.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-0-8218-3481-7
eBook: ISBN:  978-1-4704-1819-9
Product Code:  STML/23.B
List Price: $108.00 $83.50
Lectures on Generating Functions
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Lectures on Generating Functions
S. K. Lando Independent University of Moscow, Moscow, Russia
Softcover ISBN:  978-0-8218-3481-7
Product Code:  STML/23
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-1819-9
Product Code:  STML/23.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-0-8218-3481-7
eBook ISBN:  978-1-4704-1819-9
Product Code:  STML/23.B
List Price: $108.00 $83.50
  • Book Details
     
     
    Student Mathematical Library
    Volume: 232003; 148 pp
    MSC: Primary 05;

    This book introduces readers to the language of generating functions, which nowadays, is the main language of enumerative combinatorics. The book starts with definitions, simple properties, and numerous examples of generating functions. It then discusses topics such as formal grammars, generating functions in several variables, partitions and decompositions, and the exclusion-inclusion principle. In the final chapter, the author describes applications to enumeration of trees, plane graphs, and graphs embedded in two-dimensional surfaces.

    Throughout the book, the author motivates readers by giving interesting examples rather than general theories. It contains numerous exercises to help students master the material. The only prerequisite is a standard calculus course. The book is an excellent text for a one-semester undergraduate course in combinatorics.

    Readership

    Advanced undergraduates, graduate students, and research mathematicians interested in modern methods of combinatorics.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Formal power series and generating functions. Operations with formal power series. Elementary generating functions
    • Chapter 2. Generating functions for well-known sequences
    • Chapter 3. Unambiguous formal grammars. The Lagrange theorem
    • Chapter 4. Analytic properties of functions represented as power series and their asymptotics of their coefficients
    • Chapter 5. Generating functions of several variables
    • Chapter 6. Partitions and decompositions
    • Chapter 7. Dirichlet generating functions and the inclusion-exclusion principle
    • Chapter 8. Enumeration of embedded graphs
    • Final and bibliographical remarks
  • Reviews
     
     
    • A crisp and sophisticated text ... More examples than general theory. Covers standard material, but digs deeper ... An enjoyable read for professionals.

      MAA Monthly
    • (This book) is driven by very, very interesting problems and examples.

      MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 232003; 148 pp
MSC: Primary 05;

This book introduces readers to the language of generating functions, which nowadays, is the main language of enumerative combinatorics. The book starts with definitions, simple properties, and numerous examples of generating functions. It then discusses topics such as formal grammars, generating functions in several variables, partitions and decompositions, and the exclusion-inclusion principle. In the final chapter, the author describes applications to enumeration of trees, plane graphs, and graphs embedded in two-dimensional surfaces.

Throughout the book, the author motivates readers by giving interesting examples rather than general theories. It contains numerous exercises to help students master the material. The only prerequisite is a standard calculus course. The book is an excellent text for a one-semester undergraduate course in combinatorics.

Readership

Advanced undergraduates, graduate students, and research mathematicians interested in modern methods of combinatorics.

  • Chapters
  • Chapter 1. Formal power series and generating functions. Operations with formal power series. Elementary generating functions
  • Chapter 2. Generating functions for well-known sequences
  • Chapter 3. Unambiguous formal grammars. The Lagrange theorem
  • Chapter 4. Analytic properties of functions represented as power series and their asymptotics of their coefficients
  • Chapter 5. Generating functions of several variables
  • Chapter 6. Partitions and decompositions
  • Chapter 7. Dirichlet generating functions and the inclusion-exclusion principle
  • Chapter 8. Enumeration of embedded graphs
  • Final and bibliographical remarks
  • A crisp and sophisticated text ... More examples than general theory. Covers standard material, but digs deeper ... An enjoyable read for professionals.

    MAA Monthly
  • (This book) is driven by very, very interesting problems and examples.

    MAA Reviews
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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